{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.353014Z",
     "start_time": "2025-08-01T10:05:44.349324Z"
    }
   },
   "source": [
    "def f(x):\n",
    "    return 2 * x ** 2 - x **3 / 3"
   ],
   "outputs": [],
   "execution_count": 61
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.367253Z",
     "start_time": "2025-08-01T10:05:44.361645Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "\n",
    "x = np.linspace(-2, 4, 25)\n",
    "x"
   ],
   "id": "2e480e6ee0c27e2e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.  , -1.75, -1.5 , -1.25, -1.  , -0.75, -0.5 , -0.25,  0.  ,\n",
       "        0.25,  0.5 ,  0.75,  1.  ,  1.25,  1.5 ,  1.75,  2.  ,  2.25,\n",
       "        2.5 ,  2.75,  3.  ,  3.25,  3.5 ,  3.75,  4.  ])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 62
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.383826Z",
     "start_time": "2025-08-01T10:05:44.378264Z"
    }
   },
   "cell_type": "code",
   "source": [
    "y = f(x)\n",
    "\n",
    "y"
   ],
   "id": "775ec21e75417bee",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.66666667,  7.91145833,  5.625     ,  3.77604167,  2.33333333,\n",
       "        1.265625  ,  0.54166667,  0.13020833,  0.        ,  0.11979167,\n",
       "        0.45833333,  0.984375  ,  1.66666667,  2.47395833,  3.375     ,\n",
       "        4.33854167,  5.33333333,  6.328125  ,  7.29166667,  8.19270833,\n",
       "        9.        ,  9.68229167, 10.20833333, 10.546875  , 10.66666667])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 63
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.478164Z",
     "start_time": "2025-08-01T10:05:44.392833Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize = (10, 6))\n",
    "plt.plot(x, y, 'ro')"
   ],
   "id": "9a6602066b12b82e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20b23bbe5d0>]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 64
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.505761Z",
     "start_time": "2025-08-01T10:05:44.498172Z"
    }
   },
   "cell_type": "code",
   "source": [
    "beta = np.cov(x, y, ddof=0)[0, 1] / np.var(x)\n",
    "beta"
   ],
   "id": "94f812be3a0a48b5",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.0541666666666667)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 65
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.559625Z",
     "start_time": "2025-08-01T10:05:44.554779Z"
    }
   },
   "cell_type": "code",
   "source": [
    "alpha = y.mean() - beta * x.mean()\n",
    "alpha"
   ],
   "id": "1a4dea03580445d5",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(3.8625000000000003)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 66
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.577199Z",
     "start_time": "2025-08-01T10:05:44.572187Z"
    }
   },
   "cell_type": "code",
   "source": [
    "y_ = alpha + beta * x\n",
    "MSE = ((y - y_) ** 2).mean()\n",
    "MSE"
   ],
   "id": "960221af84e4fbbd",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(10.721953125)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 67
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.693547Z",
     "start_time": "2025-08-01T10:05:44.588023Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.figure(figsize = (10, 6))\n",
    "plt.plot(x, y, 'ro', label = 'sample data')\n",
    "plt.plot(x, y_, lw =3.0, label = 'linear regression')\n",
    "plt.legend()"
   ],
   "id": "442d79e38cb17bbd",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x20b23ba1820>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 68
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.887447Z",
     "start_time": "2025-08-01T10:05:44.702566Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.figure(figsize = (10, 6))\n",
    "\n",
    "plt.plot(x, y, 'ro', label = 'sample data')\n",
    "\n",
    "for deg in [1, 2, 3]:\n",
    "    reg = np.polyfit(x, y, deg)\n",
    "    y_ = np.polyval(reg, x)\n",
    "    MSE = ((y - y_) ** 2).mean()\n",
    "    print(f'deg = {deg}, MSE = {MSE:.5f}')\n",
    "    plt.plot(x, np.polyval(reg, x), label = f'deg = {deg}')\n",
    "\n",
    "plt.legend()"
   ],
   "id": "cfed87ee286222f9",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "deg = 1, MSE = 10.72195\n",
      "deg = 2, MSE = 2.31258\n",
      "deg = 3, MSE = 0.00000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x20b23fcb1a0>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 69
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:05:44.900861Z",
     "start_time": "2025-08-01T10:05:44.896458Z"
    }
   },
   "cell_type": "code",
   "source": "reg",
   "id": "8d5a3a8134bd109a",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.33333333e-01,  2.00000000e+00,  6.89327706e-16, -9.94759830e-15])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 70
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Neural Network",
   "id": "c435288158f37acf"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:15:16.899474Z",
     "start_time": "2025-08-01T10:15:12.576495Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sklearn.neural_network import MLPRegressor\n",
    "\n",
    "model = MLPRegressor(hidden_layer_sizes=3 * [256], learning_rate_init=0.03, max_iter=5000, random_state=1000)"
   ],
   "id": "70cc2c204683fe14",
   "outputs": [],
   "execution_count": 71
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:15:50.226674Z",
     "start_time": "2025-08-01T10:15:49.659047Z"
    }
   },
   "cell_type": "code",
   "source": "%time model.fit(x.reshape(-1, 1), y)",
   "id": "7db692399963d7cc",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: total: 844 ms\n",
      "Wall time: 545 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLPRegressor(hidden_layer_sizes=[256, 256, 256], learning_rate_init=0.03,\n",
       "             max_iter=5000, random_state=1000)"
      ],
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  display: none;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  overflow: visible;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".estimator-table summary {\n",
       "    padding: .5rem;\n",
       "    font-family: monospace;\n",
       "    cursor: pointer;\n",
       "}\n",
       "\n",
       ".estimator-table details[open] {\n",
       "    padding-left: 0.1rem;\n",
       "    padding-right: 0.1rem;\n",
       "    padding-bottom: 0.3rem;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table {\n",
       "    margin-left: auto !important;\n",
       "    margin-right: auto !important;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table tr:nth-child(odd) {\n",
       "    background-color: #fff;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table tr:nth-child(even) {\n",
       "    background-color: #f6f6f6;\n",
       "}\n",
       "\n",
       ".estimator-table .parameters-table tr:hover {\n",
       "    background-color: #e0e0e0;\n",
       "}\n",
       "\n",
       ".estimator-table table td {\n",
       "    border: 1px solid rgba(106, 105, 104, 0.232);\n",
       "}\n",
       "\n",
       ".user-set td {\n",
       "    color:rgb(255, 94, 0);\n",
       "    text-align: left;\n",
       "}\n",
       "\n",
       ".user-set td.value pre {\n",
       "    color:rgb(255, 94, 0) !important;\n",
       "    background-color: transparent !important;\n",
       "}\n",
       "\n",
       ".default td {\n",
       "    color: black;\n",
       "    text-align: left;\n",
       "}\n",
       "\n",
       ".user-set td i,\n",
       ".default td i {\n",
       "    color: black;\n",
       "}\n",
       "\n",
       ".copy-paste-icon {\n",
       "    background-image: url();\n",
       "    background-repeat: no-repeat;\n",
       "    background-size: 14px 14px;\n",
       "    background-position: 0;\n",
       "    display: inline-block;\n",
       "    width: 14px;\n",
       "    height: 14px;\n",
       "    cursor: pointer;\n",
       "}\n",
       "</style><body><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>MLPRegressor(hidden_layer_sizes=[256, 256, 256], learning_rate_init=0.03,\n",
       "             max_iter=5000, random_state=1000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>MLPRegressor</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.7/modules/generated/sklearn.neural_network.MLPRegressor.html\">?<span>Documentation for MLPRegressor</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\" data-param-prefix=\"\">\n",
       "        <div class=\"estimator-table\">\n",
       "            <details>\n",
       "                <summary>Parameters</summary>\n",
       "                <table class=\"parameters-table\">\n",
       "                  <tbody>\n",
       "                    \n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('loss',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">loss&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;squared_error&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"user-set\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('hidden_layer_sizes',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">hidden_layer_sizes&nbsp;</td>\n",
       "            <td class=\"value\">[256, 256, ...]</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('activation',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">activation&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;relu&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('solver',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">solver&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;adam&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('alpha',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">alpha&nbsp;</td>\n",
       "            <td class=\"value\">0.0001</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('batch_size',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">batch_size&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;auto&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('learning_rate',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">learning_rate&nbsp;</td>\n",
       "            <td class=\"value\">&#x27;constant&#x27;</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"user-set\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('learning_rate_init',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">learning_rate_init&nbsp;</td>\n",
       "            <td class=\"value\">0.03</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('power_t',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">power_t&nbsp;</td>\n",
       "            <td class=\"value\">0.5</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"user-set\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('max_iter',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">max_iter&nbsp;</td>\n",
       "            <td class=\"value\">5000</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('shuffle',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">shuffle&nbsp;</td>\n",
       "            <td class=\"value\">True</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"user-set\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('random_state',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">random_state&nbsp;</td>\n",
       "            <td class=\"value\">1000</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('tol',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">tol&nbsp;</td>\n",
       "            <td class=\"value\">0.0001</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('verbose',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">verbose&nbsp;</td>\n",
       "            <td class=\"value\">False</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('warm_start',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">warm_start&nbsp;</td>\n",
       "            <td class=\"value\">False</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('momentum',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">momentum&nbsp;</td>\n",
       "            <td class=\"value\">0.9</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('nesterovs_momentum',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">nesterovs_momentum&nbsp;</td>\n",
       "            <td class=\"value\">True</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('early_stopping',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">early_stopping&nbsp;</td>\n",
       "            <td class=\"value\">False</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('validation_fraction',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">validation_fraction&nbsp;</td>\n",
       "            <td class=\"value\">0.1</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('beta_1',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">beta_1&nbsp;</td>\n",
       "            <td class=\"value\">0.9</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('beta_2',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">beta_2&nbsp;</td>\n",
       "            <td class=\"value\">0.999</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('epsilon',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">epsilon&nbsp;</td>\n",
       "            <td class=\"value\">1e-08</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('n_iter_no_change',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">n_iter_no_change&nbsp;</td>\n",
       "            <td class=\"value\">10</td>\n",
       "        </tr>\n",
       "    \n",
       "\n",
       "        <tr class=\"default\">\n",
       "            <td><i class=\"copy-paste-icon\"\n",
       "                 onclick=\"copyToClipboard('max_fun',\n",
       "                          this.parentElement.nextElementSibling)\"\n",
       "            ></i></td>\n",
       "            <td class=\"param\">max_fun&nbsp;</td>\n",
       "            <td class=\"value\">15000</td>\n",
       "        </tr>\n",
       "    \n",
       "                  </tbody>\n",
       "                </table>\n",
       "            </details>\n",
       "        </div>\n",
       "    </div></div></div></div></div><script>function copyToClipboard(text, element) {\n",
       "    // Get the parameter prefix from the closest toggleable content\n",
       "    const toggleableContent = element.closest('.sk-toggleable__content');\n",
       "    const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';\n",
       "    const fullParamName = paramPrefix ? `${paramPrefix}${text}` : text;\n",
       "\n",
       "    const originalStyle = element.style;\n",
       "    const computedStyle = window.getComputedStyle(element);\n",
       "    const originalWidth = computedStyle.width;\n",
       "    const originalHTML = element.innerHTML.replace('Copied!', '');\n",
       "\n",
       "    navigator.clipboard.writeText(fullParamName)\n",
       "        .then(() => {\n",
       "            element.style.width = originalWidth;\n",
       "            element.style.color = 'green';\n",
       "            element.innerHTML = \"Copied!\";\n",
       "\n",
       "            setTimeout(() => {\n",
       "                element.innerHTML = originalHTML;\n",
       "                element.style = originalStyle;\n",
       "            }, 2000);\n",
       "        })\n",
       "        .catch(err => {\n",
       "            console.error('Failed to copy:', err);\n",
       "            element.style.color = 'red';\n",
       "            element.innerHTML = \"Failed!\";\n",
       "            setTimeout(() => {\n",
       "                element.innerHTML = originalHTML;\n",
       "                element.style = originalStyle;\n",
       "            }, 2000);\n",
       "        });\n",
       "    return false;\n",
       "}\n",
       "\n",
       "document.querySelectorAll('.fa-regular.fa-copy').forEach(function(element) {\n",
       "    const toggleableContent = element.closest('.sk-toggleable__content');\n",
       "    const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';\n",
       "    const paramName = element.parentElement.nextElementSibling.textContent.trim();\n",
       "    const fullParamName = paramPrefix ? `${paramPrefix}${paramName}` : paramName;\n",
       "\n",
       "    element.setAttribute('title', fullParamName);\n",
       "});\n",
       "</script></body>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 72
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:23:06.899118Z",
     "start_time": "2025-08-01T10:23:06.891446Z"
    }
   },
   "cell_type": "code",
   "source": [
    "y_ = model.predict(x.reshape(-1, 1))\n",
    "\n",
    "MSE = ((y - y_) ** 2).mean()\n",
    "MSE"
   ],
   "id": "c970d6bbd6883dc2",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.006775846547443183)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 75
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-08-01T10:24:03.157265Z",
     "start_time": "2025-08-01T10:24:03.041667Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.figure(figsize = (10, 6))\n",
    "plt.plot(x, y, 'ro', label = 'sample data')\n",
    "plt.plot(x, y_, lw =3.0, label = 'dnn estimation')\n",
    "plt.legend()"
   ],
   "id": "8a82b86a10f2716c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x20b3d3969f0>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 76
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
